document.write( "Question 979070: An aeroplane flies 3500 km in the same time a train covers 600 km.If the speed of the aeroplane is 50 km/h more than five times the speed of the train ,what are the speeds of the train and the aeroplane? \n" ); document.write( "
Algebra.Com's Answer #600361 by Theo(13342)\"\" \"About 
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rate * t = distance
\n" ); document.write( "rt = d
\n" ); document.write( "for the plane:
\n" ); document.write( "rt = d becomes rt = 3500
\n" ); document.write( "for the train:
\n" ); document.write( "rt = d becomes rt = 600
\n" ); document.write( "since the time each takes is the same, we'll solve for t.
\n" ); document.write( "for the plane, t = d/r = 3500/r
\n" ); document.write( "for the train, t = d/r = 600/r
\n" ); document.write( "since t is the same for each, then t = t, or their equivalents:
\n" ); document.write( "3500/r = 600/r
\n" ); document.write( "the rates are different, so we'll need to distinguish beween the two rates.
\n" ); document.write( "we'll call r for the plane r1.
\n" ); document.write( "we'll call r for the train r2.
\n" ); document.write( "the equation becomes:
\n" ); document.write( "3500/r1 = 600/r2
\n" ); document.write( "we are told that the plan travels 5 times as fast as the train plus 50 km/hr.
\n" ); document.write( "the equation for that is:
\n" ); document.write( "r1 = 5r2 + 50
\n" ); document.write( "we'll replace r1 with 5r2 + 50 in the equation of 3500/r1 = 600/r2 to get:
\n" ); document.write( "3500 / (5r2+50) = 600 / r2
\n" ); document.write( "we'll cross multiply to get:
\n" ); document.write( "3500 * r2 = 600 * (5r2 + 50)
\n" ); document.write( "simplify to get:
\n" ); document.write( "3500r2 = 3000r2 + 30000
\n" ); document.write( "subtract 3000r2 from both sides of this equation to get:
\n" ); document.write( "500r2 = 30000
\n" ); document.write( "solve for r2 to get:
\n" ); document.write( "r2 = 60
\n" ); document.write( "since r1 = 5r2 + 50, this means that r1 = 350.
\n" ); document.write( "the train travels at 60 kmph.
\n" ); document.write( "the plan travels at 350kmph.
\n" ); document.write( "now that we know the rates and distance, we can solve for time.
\n" ); document.write( "for the plane:
\n" ); document.write( "350*t = 3500
\n" ); document.write( "solve for t to get t = 10 hours.
\n" ); document.write( "for the train:
\n" ); document.write( "60*t = 600
\n" ); document.write( "solve for t to get 10 hours.
\n" ); document.write( "the time for both is 10 hours as it should be since they both took the same amount of time.
\n" ); document.write( "this confirms our calculations are correct.
\n" ); document.write( "our solution is:
\n" ); document.write( "the plane travels at 350kmph
\n" ); document.write( "the train travels at 60kmph \n" ); document.write( "
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